Geometry Chapter 4: Classifying Triangles

Triangle Classifications

• Acute Triangle: Contains three acute angles, each less than 90 degrees.
• Equiangular Triangle: Features three congruent acute angles, thereby also being an acute triangle.
• Right Triangle: Characterized by having one right angle, equal to 90 degrees.
• Obtuse Triangle: Contains one obtuse angle, which is greater than 90 degrees but less than 180 degrees.
• Equilateral Triangle: Distinguished by having three congruent sides and angles, each measuring 60 degrees.
• Isosceles Triangle: Comprises at least two congruent sides and the angles opposite those sides are also congruent.
• Scalene Triangle: No sides or angles are congruent, making all sides and angles different in measurement.

Angle Definitions

• Interior: Refers to all points located within the triangle itself.
• Exterior: Comprises all points that lie outside the triangle.

Angle Relationships

• Interior Angle: Formed by the intersection of two sides of the triangle.
• Exterior Angle: Created by one side of the triangle and the extension of an adjacent side.
• Remote Interior Angle: An interior angle that is not adjacent to the corresponding exterior angle.

Theorems

• Exterior Angle Theorem: States that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
• Third Angles Theorem: Indicates that if two angles of one triangle are congruent to two angles of another triangle, then the third angles in both triangles are also congruent.

This quiz focuses on the classification of triangles, covering various types such as acute, equiangular, right, obtuse, equilateral, and isosceles triangles. Each flashcard provides definitions and characteristics of these triangle types. Test your knowledge of triangle properties in this engaging quiz.